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We provide a Faddeev-Reshetikhin-Takhtajan's RTT approach to the quantumgroup Fun(GL_{r,s}(n)) and the quantum enveloping algebra U_{r,s}(gl_n)corresponding to the two-parameter R-matrix. We prove that the quantumdeterminant det_{r,s}T is a quasi-central element in Fun(GL_{r,s}(n))generalizing earlier results of Dipper-Donkin and Du-Parshall-Wang. Theexplicit formulation provides an interpretation of the deforming parameters,and the quantized algebra U_{r,s}(R) is identified to U_{r,s}(gl_n) as the dualalgebra. We then construct n-1 quasi-central elements in U_{r,s}(R) which areanalogues of higher Casimir elements in U_q(gl_n).

R-matrix realization of two-parameter quantum group U_{r,s}(gl_n)